“IPIX 360 Suite” is a commercial name of a commercially available system presented by Minds-Eye-View Inc. This system, hereafter simply called “IPIX” in this application, deals with input and output of surface information of, in particular, spheres among various 3-D objects. This system can generate spherical information by virtually coupling two circular fisheye images together. Users can get a view of any partial portion of the spherical information by moving a rectangular viewer from one place to another.
Among various existing techniques for flattening out a spherical image on a rectangular plane, cylindrical projections directed to producing a world map can display the entire surface of the earth on a rectangular flat plane by projecting the earth's surface onto a cylinder circumscribing the equator and then unfolding the cylinder. Mercator projection is a conformal projection, and equal-area cylindrical projection is an equal-area projection. Panorama photography is an analogous art that captures images of some divisional parts of the entire view of 360 degrees and assembles these images on a virtual cylinder.
In 1879, Charles Sanders Peirce of the United States Coast and Geodetic Survey proposed a quincuncial projection. This quincuncial projection, hereafter called “Peirce's projection” in this application, can provide a square or 1:2 rectangular conformal world map and also can tessellate a plurality of such world maps on a plane. Geographical information properly matches between adjacent world maps tessellated on the plane.
As a scheme of polyhedral projection, Laurence P. Lee at National Mapping Agency in New Zealand proposed in 1965 a conformal world map of an equilateral triangle made by triangular projection that projects the earth's surface on a tetrahedron and then developing the tetrahedron. This is hereafter called “Lee's Projection” in this application.
As a technique for correcting distortion of a flattened image converted from spherical information, Buckminster Fuller presented a cartography called the Dymaxion map that has less distortion in continents' areas and shapes than any prior cartographies (see R. Buckminster Fuller, INVENTIONS: St. Martins' Press, 1983, P. 85). This cartography divides the entire spherical surface into twenty equal-area triangular regions, then projects information on respective spherical icosahedral regions onto respective triangular face of a regular icosahedron, and thereafter develops the icosahedron. Therefore, each divisional spherical region corresponds to each icosahedral face, and the ratio of the area of each divisional triangular region relative to the entire area of the sphere is equal to the ratio of each icosahedral face relative to the total surface area of the icosahedron. That is, when the surface of the earth is projected on the icosahedron, the center angle of 63′25″ of each edge of the divisional triangular region of the sphere is equally maintained as the center angle of each edge of the icosahedral face.
Collignon's Projection by Edouard Collignon proposed an equal-area world map in 1865. Here is used a pseudocylindrical projection, which maintains an original arrangement of longitudes radiating from the two poles and an original parallel arrangement of latitudes on one rhombus or two rhombuses.
Commercially available software under the commercial name of “Flexify 2” (2008 Flaming Pear Software) utilizes map projections in image processing. It can convert imported flat images such as panorama or fisheye pictures into images on any two-dimensional form according to various kinds of map projections such as Dymaxion map and the Peirce's projection, or into polyhedral images.
Japanese Patent Laid-open Publication No. JP 2003-178298 is related to correction of errors in area ratio, i.e. in solid angle, in photography. This application discloses a technique called “mesh camera” for pasting photographs taken by different types of lenses to fit with each other. The “mesh camera” technique can project such photographs onto a 3-D object called an output frame such as, for example, a regular polyhedron or sphere, while minimizing the solid angle error.
U.S. Pat. No. 6,141,034 discloses a technique which can simultaneously expose a substantially omnidirectional view by arranging externally oriented optic axes on eleven dodecahedral faces. This patent proposes arrangements of optic axes based on a tetrahedron and an octahedron to cope with stereoscopic viewing.
All of the above-mentioned existing techniques are defective in one aspect or another. Namely, the IPIX technology discussed above contains large distortions when the image is zoomed out. The distortions become too large for a user to properly figure out the subjects when the image is zoomed out to provide an approximately hemispherical visual field. Additionally, the IPIX is subjected to an undesirable phenomenon called Gimbal lock, which pertains to unnatural movements of the viewer, since the viewer rotates about a single axis.
Cylindrical projections leave distortions at bottom and top regions of world maps. Therefore, shapes of subjects in both polar regions are difficult to figure out. These projections can rearrange geographical information in the east and west directions, but cannot cope with such rearrangement in other directions without a certain complex image processing. Similarly, the panorama photography, which takes shots while rotating a camera about a single rotation axis, cannot capture objects above and below the camera position. Therefore, the panorama photography is not a technique for providing a complete omnidirectional image as well.
The Dymaxion map that is just a development of an icosahedron inevitably has a zigzag outline, so that the geographical information in the world map is difficult to figure out properly. If ocean currents are added to the world map, the currents appear discontinuous regardless of all efforts to rearrange the twenty regular triangles. Thus, the Dymaxion map cannot pack geographical information closely on a rectangular plane that is an ideal map format.
Among regular polyhedra, the icosahedron employed in the Dymaxion projection can divide an omnidirectional image into 20 equal parts and can distribute distortions to 20 divisional regions equally. In contrast, the tetrahedron employed by the Lee's projection divides an omnidirectional image into as much less as only four parts, and results in producing strong local distortions. Therefore, in the world map by the Lee's projection, objects near the tetrahedral vertices increase in solid angle to five times or more of their original sizes. Additionally, the Lee's projection is not a proposal of a two-dimensional rectangular image. Because of the same reason, the Peirce's projection is also subjected to a large distortion.
The Collignon's Projection is an equal-area projection with a simple outline. However, it does not provide a rectangular map.
The Flexify 2, which utilizes existing map projections, involves the same problems as those of the Dymaxion map and the Peirce's projection.
JP 2003-178298 is not directed to flattening out omnidirectional images. Further, this prior art is not a proposal of a photographing technique. Instead, it relates to assembling some different shots taken by different setups into an integral image. In this prior art, one or more of prepared pictures are inevitably expanded locally when packed on a sphere or a regular polyhedron, and this produces a resulting image locally different in resolution.
U.S. Pat. No. 6,141,034 does not teach any technique to flatten out omnidirectional images. In addition, this existing art cannot obtain a complete omnidirectional view due to the lack of an optic axis toward the bottom one of dodecahedral faces.
In summary, the existing arts of one group involve the problem that a distortion is contained when an entire area of an image taken from a 3-D object such as a sphere or a polyhedron is displayed simultaneously on a rectangular flat plane; and those of another group involve the problem that, once a distortion is corrected, the outline of image can no longer closely fit in a rectangular plane of an ordinary display monitor, and produces an unused zone called vignetting on the display.
In a further review of the entire field of omnidirectional photography, existing techniques step through some of various mapping processes such as exposure, image processing and projection for display, respectively, from the stage of taking photographs up to the stage of giving a projected image of the photographs to be observed on a screen. However, any of these existing arts deals with only a part of these processes, and none of them disclose a method of consistently stepping across all mapping processes.